Heat Capacity

Introduction

Heat capacity, or thermal capacity, is a physical property of matter that describes the amount of heat energy required to change its temperature. It is an extensive property, meaning it depends on the amount of substance.

Definitions

Specific Heat Capacity

The specific heat capacity () of a substance is the amount of heat required to raise the temperature of one kilogram of the substance by one degree Celsius (or Kelvin, as the scale is identical). It is given by:

where is the heat supplied, is the mass, and is the change in temperature.

Molar Heat Capacity

The molar heat capacity () is the amount of heat required to raise the temperature of one mole of a substance by one degree Celsius. It can be defined as:

where is the number of moles.

Heat Capacity at Constant Pressure and Constant Volume

In thermodynamics, it’s often useful to define heat capacities under constant pressure () and constant volume ().

For an ideal gas, these quantities are related by Mayer’s relation:

where is the universal gas constant.

Heat Capacity and Phase Changes

During phase transitions (like melting or boiling), a substance can absorb or release heat without changing temperature. The amount of heat required to change the phase of a unit mass of the substance is known as the latent heat.

Applications and Importance

Heat capacity plays a crucial role in many areas of science and engineering, such as thermodynamics, calorimetry, and climate science. It influences how quickly an object heats up or cools down, which is vital for understanding and designing heating and cooling systems, among other applications.

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